5 A formula is an equation that states a rule for a relationship among quantities.In the formula d = rt, d is isolated. You can "rearrange" a formula to isolate any variable by using inverse operations. This is called solving for a variable.

6 Solving for a VariableStep 1 Locate the variable you are asked to solve for in the equation.Step 2 Identify the operations on this variable and the order in which they are applied.Step 3 Use inverse operations to undo operations and isolate the variable.

7 Example 1: ApplicationThe formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol  in your answer.Locate d in the equation.Since d is multiplied by , divide both sides by  to undo the multiplication.Now use this formula and the information given in the problem.

8 Example 1: Application ContinuedThe formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol  in your answer.Now use this formula and the information given in the problem.The bowl's diameter is inches.

9 Check It Out! Example 1Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.d = rtLocate t in the equation.Since t is multiplied by r, divide both sides by r to undo the multiplication.Now use this formula and the information given in the problem.

10 Check It Out! Example 1Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.Van Dyk’s time was about 1.46 hours.

11 Example 2A: Solving Formulas for a VariableThe formula for the area of a triangle is A = bh,where b is the length of the base, and h is the height. Solve for h.A = bhLocate h in the equation.Since bh is multiplied by , divide both sides by to undo the multiplication.2A = bhSince h is multiplied by b, divide both sides by b to undo the multiplication.

12 Dividing by a fraction is the same as multiplying by the reciprocal.Remember!

13 Example 2B: Solving Formulas for a VariableThe formula for a person’s typing speed is,where s is speed in words per minute,w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.Locate e in the equation.Since w–10e is divided by m, multiply both sides by m to undo the division.ms = w – 10eSince w is added to –10e, subtract w from both sides to undo the addition.–w –wms – w = –10e

14 Example 2B: Solving Formulas for a VariableThe formula for a person’s typing speed is,where s is speed in words per minute,w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.Since e is multiplied by –10, divide both sides by –10 to undo the multiplication.

15 Dividing by a fraction is the same as multiplying by the reciprocal.Remember!

16 Check It Out! Example 2The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.f = i – gtLocate i in the equation.f = i – gt+ gt gtSince gt is subtracted from i, add gt to both sides to undo the subtraction.f + gt = i

17 A formula is a type of literal equationA formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.

20 Check It Out! Example 3bSolve for VLocate V in the equation.Since m is divided by V, multiply both sides by V to undo the division.VD = mSince V is multiplied by D, divide both sides by D to undo the multiplication.

22 Lesson Quiz: Part 2Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.6. Solve Euler’s formula for F.F = 2 – V + E7. How many faces does a polyhedron with 8 vertices and 12 edges have?6